#### Q09 Part V: Linear Regression • Name:

Lane lengths
Lane | Length/m |

1 | 421 |

2 | 426 |

3 | 431 |

4 | 434 |

5 | 444 |

6 | 460 |

7 | 458 |

6 | 452 |

5 | 447 |

4 | 436 |

3 | 428 |

2 | 423 |

1 | 410 |

Using a Global Positioning Satellite unit I ran laps at the Pohnpei state track up at PICS starting in lane one and moving out by one lane per lap until the seventh lane and then I moved in by one lane per lap. The data is given in the table. The first column is the lane number, the second column is the length of that lane.

- _________ Determine the sample size of the lane length in meters.
- _________ Determine the minimum lane length in meters.
- _________ Determine the maximum lane length in meters.
- _________ Determine the range of the lane length in meters.
- _________ Determine the mode of the lane lengths in meters.
- _________ Determine the median of the lane lengths in meters.
- _________ Determine the mean of the lane lengths in meters.
- _________ Determine the standard deviation of the lane lengths in meters.
- _________ Determine the coefficient of variation of the lane lengths in meters.
- _________ Calculate the slope of the best fit (least squares) line.
- _________ Calculate the y-intercept of the best fit (least squares) line.
- _________ Is the correlation positive, negative, or neutral?
- _________ Use the equation of the best fit line to calculate the predicted lane length for lane eight.
- _________ If there was a lane "zero", how long would lane zero be predicted to be?
- _________ Use the inverse of the best fit line to calculate the lane number which is 500 meters long (a half a kilometer).
- _________ Calculate the linear correlation coefficient r for the data.
- _________ Is the correlation none, low, moderate, high, or perfect?
- _________ Calculate the coefficient of determination.
- _________ What percent of the variation in the lane number explains the variation in the lane length?

Linear Regression Statistics |

Statistic or Parameter | Symbol | Equations | OpenOffice |

Slope | b | | =SLOPE(y data; x data) |

Intercept | a | | =INTERCEPT(y data; x data) |

Correlation | r | | =CORREL(y data; x data) |

Coefficient of Determination | r^{2} | |
=(CORREL(y data; x data))^2 |